2.1 Archaeological selection criteria

A primary requirement when selecting potsherds for radiocarbon dating is a detailed understanding of their archaeological context. Sample selection is critically dependent on the objectives of the study and the methodology that will be employed for the interpretation of the results (Bayliss and Marshall Reference Bayliss and Marshall2022, §3).

Sherds may be of intrinsic interest, because they are typologically diagnostic or contain dietary or other information. For instance, if the research question focuses on refining and anchoring relative typochronologies to provide calendrical timescales for the occurrence of particular vessel types directly, then sample selection must focus on these typologically characteristic vessels (Casanova et al. Reference Casanova, Knowles, Bayliss, Dunne, Barański, Denaire, Lefranc, di Lernia, Roffet-Salque, Smyth, Barclay, Gillard, Claßen, Coles, Ilett, Jeunesse, Krueger, Marciniak, Minnitt, Rotunno, van de Velde, van Wijk, Cotton, Daykin and Evershed2020c). If the research question focusses on directly dating specific foodstuffs (e.g. dairy products), then potsherds with residues identified as relating to the commodities must be selected (cf. part 2.2.2) (Casanova et al. Reference Casanova, Knowles, Bayliss, Roffet-Salque, Heyd, Pyzel, Claßen, Domboroczki, Ilett, Lefranc, Jeunesse, Marciniak, van Wijk and Evershed2022a; Stojanovski et al. Reference Stojanovski, Živaljević, Dimitrijević, Dunne, Evershed, Balasse, Dowle, Hendy, McGrath and Fischer2020b). In these cases, the provenance of the samples is immaterial, as what matters is the quality of the typological or other information that is intrinsic to the sherd.

If the objective of the study is to provide dating for an archaeological site or another type of archaeological sequence (e.g. a seriation of grave-assemblages), then stricter archaeological criteria for sampling are required. In these cases, it is important to assess whether potential samples are intrusive or residual in the context from which they were recovered. Evidence that may be used to infer that sherds are not redeposited or intrusive includes (in descending order of reliability; Figure 1):

1. a. Complete vessels deposited in closed contexts (e.g. graves).

2. b. Refitting potsherds.

3. c. Non-refitting sherds judged to be from the same vessel.

4. d. Vessels where the entire profile survives.

5. e. Sherds judged to have been deliberately deposited (e.g. to line a pit).

6. f. Large sherds in fragile fabrics which are likely to have broken further if redeposited.

Figure 1 Photographs of potsherds from the early Neolithic sites of a. Rosheim “Rittergass”, France and b. Robin Hood Ball, UK with examples of 1. Refitting potsherds, 2. Non-refitting potsherds judged to be from the same vessel, 3. Single decoratively (a. Linearbandkeramik decoration) or typologically (b. carinated bowl) characteristic potsherds, and 4. Single undecorated potsherds.

These criteria are particularly important where it is intended that stratigraphy or other archaeological information will be incorporated with the radiocarbon dates using Bayesian chronological modeling to provide more precise chronologies, or when sampling from multi-period sites. They are also critical when it is not possible to sample typologically distinctive sherds (either on curatorial grounds or because they do not contain sufficient FAs), and so less distinctive material is sampled instead from the same deposits.

2.2. Selection criteria based on organic residue analysis (ORA)

2.2.2 Lipid sources and distributions

A critical first step after collection of potsherds is a prescreening using approximately 2 g of potsherd. We recommend that lipid extraction be performed using an acidic extraction (MeOH/H₂SO₄) rather than solvent extraction to maximise the lipid recovery and provide effective quantification (Correa-Ascencio and Evershed, Reference Correa-Ascencio and Evershed2014). The addition of an internal standard is essential for quantification of lipids (Correa-Ascencio and Evershed, Reference Correa-Ascencio and Evershed2014). The TLEs should be prescreened by gas chromatography (GC), GC–mass spectrometry (GC-MS) and GC–combustion–isotope ratio MS (GC-C-IRMS). At present, potsherds which are suitable for dating should be identified based on their lipid distribution according to the following criteria:

1. a. TLEs should be dominated by palmitic (C_16:0) and stearic (C_18:0) fatty acids (FAs) characteristic of degraded animal fats (Figure 2a–d). Sherds with lipids originating from different sources (potentially with reservoir offsets) should be avoided. TLEs showing the presence of other compounds such as long-chain n-alkanes or n-alkanols in appreciable abundances suggest the mixing of animal fats with other resources. Such samples do not make ideal candidates for CSRA and caution should be exercised (Figure 2e–f).

2. b. Lipid abundance should be over 500 µg of lipids per gram of sherd, which translates to sampling ∼5 g of potsherds for CSRA. Lower concentrations down to 250 µg g^–1 of sherd can be targeted, but this means up to 10 g of sherd will be required and there is more potential for inhomogeneous lipid partitioning.

3. c. Ideally, C_16:0 and C_18:0 FAs should be present in relatively equal abundances to allow isolation of the same quantity of each compound (Figure 2a–b). This criterion is unlikely to be met for all TLEs, since the relative abundance of the two FAs depends on the source of animal fat and diagenetic state (Figure 2c–d) (Casanova et al. Reference Casanova, Knowles, Outram, Stear, Roffet-Salque, Zaibert, Logvin, Shevnina and Evershed2022c).

4. d. FAs must derive from terrestrial animals. This can be determined using the δ¹³C_16:0 and δ¹³C_18:0 values determined by GC-C-IRMS together with screening for aquatic biomarkers by GC/MS with SIM (selective ion monitoring) mode (Casanova et al. Reference Casanova, Knowles, Ford, Cramp, Sharples and Evershed2020b; Cramp and Evershed Reference Cramp and Evershed2014), examination of faunal remains, and consideration of site location to ensure no reservoir effects will affect the ¹⁴C dates.

Figure 2 Partial gas chromatograms of potsherds with concentrations suitable for ¹⁴C dating for a. ROS-C-4694 b. ROS-C-4682 c. ROS-C-4701 d. ROS-C-4677 exhibiting “pure” animal fats and various ratios of the C_16:0 and C_18:0 fatty acids, e. ROS-C-4615 showing a mixture of animal fat and beeswax and f. ROS-C-4617 showing a dominance of beeswax. IS is the internal standard and numbers corresponds to the carbon chain lengths of the various alkyl lipids.

Pottery used to process aquatic resources only or the mixing of terrestrial and aquatic resources can also be CSRA dated but this adds complexity compared to FAs of terrestrial origin as it requires quantification and correction for aquatic reservoir effects (cf. part 5.2). It is also possible to target biomarker lipids other than FAs, such as n-alkanes in the case of the presence beeswax (Figure 2f) or plant residues. The compound(s) of interest need to be present at high enough concentrations for CSRA. Furthermore, targeting other classes of compounds will necessitate making changes to the chromatographic and trapping parameters required for the isolation of new compounds (cf. part 3.3). These modified methods will require full re-validation as they may affect factors such as trapping efficiency, cross-contamination in the pcGC (notably, the syringe and trapping capillaries), and column bleed etc.

2.3 Case Study 1: Consideration of the number of required potsherds for CSRA

We provide here an example of a “typical” application of CSRA using a regional collection of pottery from seven sites dating from the 6th to 4th millennium BC in Alsace, France (Casanova et al. Reference Casanova, Arbogast, Denaire, Jeunesse, Lefranc and Evershed2020a). Table 1 summarises ORA results of 871 potsherds indicating the lipid profiles defined as ‘pure’ terrestrial animal fats, the sherds from refined decorated vessels and undecorated vessels, including refitting sherds, containing lipid concentrations >500 µg.g^–1. This level of evaluation is essential for assessing the suitability of pottery assemblages and pinpointing specific potsherds, for CSRA (Table 1).

Table 1 Table showing the numbers of potsherds: analyzed per site, containing animal fats, with concentration >500 µg.g^-1, and suitable for ¹⁴C dating for the overall assemblage, refitted, decorated and undecorated sherds. The percentages are calculated for the total number of sherds per category except for the bold values that are the percentage of the total number of sherds analyzed per site. BIS = Bischoffsheim, ROS = Rosheim, COL = Colmar, ENS = Ensisheim, SIE = Sierentz, LBK = Linearbandkeramik (early Neolithic), Gro. = Grossgartach (Middle Neolithic), Roe. = Roessen (Middle Neolithic)

Of the 871 potsherds analyzed, a total of 88 sherds, or 10%, were regarded as suitable for ¹⁴C dating if sherd size allowed. The proportion of potsherds datable from each site varies between 2% and 28%. Overall, the frequency of undecorated vessels was found to be better than decorated pottery vessels in meeting the criteria for CSRA, i.e. 83 undecorated versus 5 decorated potsherds. The highest lipid concentrations defined as “pure” animal products were recovered predominantly from undecorated pottery vessels, while decorated vessels showed lower lipid concentrations and more complex mixed animal and plant/beeswax lipid profiles. This difference supports hypotheses surrounding vessel specialisation, with undecorated vessels being most commonly used as utilitarian cooking pots while the decorated vessels were more likely used as table wares. Focussing only on the undecorated (cooking vessels) then 15% of sherds from this category were suitable for dating using CSRA, which is typical for many prehistoric assemblages.

Variations in the proportion of datable potsherds in assemblages derived from contemporaneous sites, even those in close proximity and of the same cultural group (Linearbandkermik (LBK) culture), highlight the influence of the burial and diagenesis on lipid preservation. For example, the site of Colmar showed poor lipid preservation with 3% of the undecorated sherds being datable, while other LBK settlements reached up to 17%. There is also temporal variation for lipid preservation from the same locality as illustrated by Rosheim. The proportion of datable undecorated potsherds is 17% for the LBK (ca. 5500 BC), 33% for the Grossgartach (ca. 4600 BC) and 32% for the Roessen (ca. 4400 BC). The higher proportion of sherds suitable for CSRA in the younger deposits may point to differences in cooking practices between the cultural groups.

The overall dataset shows that cooking vessels are the best candidates for CSRA. The results also suggest that, ca. 3 to 10 times the number of potsherds targeted for radiocarbon dating should be analyzed by ORA to identify sufficient suitable samples for a dating programme.

3.1 Extraction of FAs from potsherds

Once the potsherds have been selected for CSRA, lipids are extracted from the ceramic matrix using an acidified solution of methanol (Correa-Ascencio and Evershed, Reference Correa-Ascencio and Evershed2014) employing a protocol optimised for larger ceramic samples, up to 10 g (Casanova et al. Reference Casanova, Knowles, Bayliss, Dunne, Barański, Denaire, Lefranc, di Lernia, Roffet-Salque, Smyth, Barclay, Gillard, Claßen, Coles, Ilett, Jeunesse, Krueger, Marciniak, Minnitt, Rotunno, van de Velde, van Wijk, Cotton, Daykin and Evershed2020c). The processing of potsherds proceeds as follows:

1. a. Removal of surface contaminants from the exterior of the potsherd using a modeling drill (Figure 3ai). The cleaned piece is handled with tweezers (to avoid contamination from fingers or gloves), sub-sampled using a hammer and chisel, crushed to a fine powder using a pestle and mortar then transferred to one or several culture tubes depending on the mass of ceramic powder.

2. b. The lipids are simultaneously extracted, and the FAs methylated to fatty acid methyl esters (FAMEs) using a methanolic solution of sulphuric acid (4% v/v, 3 × 8 mL, 1 hr, 70^oC; Figure 3aii). To ensure all lipids are recovered, especially when extracting large amounts of clay regular mixing is performed and the extraction performed three times in total.

3. c. The three acid extracts are transferred to a test tube, centrifuged (10 min, 2500 rpm) and combined in a larger culture tube containing 5mL of MQ-water. The lipids are then extracted from the acidic aqueous phase using n-hexane (4 × 5 mL), which is transferred into 3.5 mL vials, and blown down to dryness under a gentle N₂ stream. If an emulsion is visible in the centrifuge tubes further centrifugation is undertaken (5 min, 2000 rpm) before decanting the n-hexane fractions for evaporation.

4. d. The vials are weighed empty, and after concentration of the lipids extracted to roughly estimate the recovery of lipids. TLEs are stored dried and sealed with PTFE tape in the fridge before pcGC isolation.

3.2 Assessing and eliminating contamination in the PCGC instrument

Prior to the isolation of the FAs in the pcGC instrument, sources of contamination should be quantified and suppressed. To achieve this, we recommend the following:

1. a. Verifying that the GC column stationary phase “bleed” is not contributing significant C to samples by its quantification. This can be achieved using the method described in Casanova et al. (Reference Casanova, Knowles, Williams, Crump and Evershed2017). This should be performed every time a new column is fitted, and when changing the trapping parameters to isolate higher molecular weight compounds. For FAME isolation, we utilise a non-polar column (100% dimethylpolysiloxane, 1.5 µm film thickness, 30 m, Restek) as it allows injection of concentrated lipid extracts and demonstrates minimal column “bleed”. Other “low bleed” columns from other suppliers are likely also suitable for the method, but have not been tested by us.

2. b. Use of our solventless trapping system (STS; Figure 3aiii) consisting of a plug of furnaced glass wool (∼1 cm) held in a glass capillary tube (Casanova et al. Reference Casanova, Knowles, Williams, Crump and Evershed2018). The standard U-tube trap design should be avoided as it requires use of organic solvent to recover the trapped compounds. Our NMR studies have shown this solvent remains trapped within the isolated FAME sample, which introduces offsets in the ¹⁴C results. In addition, we showed the average FAME recovery with the STS is 95.7% (Casanova et al. Reference Casanova, Knowles, Williams, Crump and Evershed2018).

3. c. Elimination of carryover effects between samples in the instrument by cleaning the syringe, changing the waste solvent, and baking the column at 300^oC for 20 min. The residual FAs in the capillaries connecting the preparative unit to the traps must be cleaned using a heat gun then wiped with ethanol. If further contamination is visible (e.g. particulate graphite from ferrules) after cleaning, then the capillaries must be trimmed or replaced before proceeding.

4. d. In the absence of standards and blanks of the same compounds (with the same chromatographic and trapping parameters), pseudo-processing standards and blanks should be employed. This is achieved by injection of n-hexane, and trapping the same chromatographic elution “windows” as for the analyte compounds (C_{16 :0} and C_18:0 FAMEs). After transfer of the glass wool (containing any column bleed or other contamination arising from processing that would be present in samples) to foil capsules, a standard or blank (e.g. IAEA C-7, phthalic anhydride blank etc.) is added to the same capsule to obtain the pseudo processed standards. We have also created C_16:0 and C_18:0 FA ¹⁴C standards from bog butter for use as full processing standards for CSRA (Casanova et al. Reference Casanova, Knowles, Mulhall, Sikora, Smyth and Evershed2021). Once the, current intercomparison exercise on these materials is completed, these standards will be made available to the scientific dating community upon request to the National Museum of Ireland.

3.3 Isolation of FAs by PCGC

Successful isolation of FAMEs requires rigorous assessment of (i) chromatographic quality, (ii) the concentration of FAs in the extract solutions, and (iii) retention times of the FAs under the pcGC conditions, before setting up a trapping sequence. A short GC method of just over 20 min for each run means that one pot extract can be completed in 24 h. The critical steps in the workflow are as follows:

1. a. The TLEs must be derivatised with N,O-Bis(trimethylsilyl)trifluoroacetamide (20 µL, 1 h, 70^oC) as n-alkanols are often present (even in low concentrations) and clog the injector if not derivatised. After removal of the excess of BSTFA under a stream of N₂, the TLE is redissolved in a minimum of 80 µL n-hexane and transferred to an auto-sampler vial using a clean syringe.

2. b. Furnaced traps need to be fitted on the fraction collector, one per compound to be isolated and one for use as a “waste”’ trap. This way, if isolation is not successful, FAMEs can be recovered from the waste trap and re-isolated.

3. c. The TLE should be run once in the pcGC to assess the chromatography, allow the concentration to be adjusted to ∼5 µg.µL^–1 of individual FAMEs, and to define the trapping windows for the isolation of FAMEs based on their retention times.

4. d. A trapping sequence should be set up to isolate ∼200 µg of C per compound in 40 consecutive injections. If the relative proportion of C_16:0 and C_18:0 FAs is uneven adjust the dilution to ensure a minimum of 200 µg of C is isolated for the compound with the lowest abundance in 40 injections. If the relative proportion of the two FAs is over four, the most concentrated FAME should be isolated for fewer runs (10, for example), the trap replaced with a new one to complete the isolation of the second FAME (Casanova et al. Reference Casanova, Knowles, Outram, Stear, Roffet-Salque, Zaibert, Logvin, Shevnina and Evershed2022c). This will prevent the isolation of substantially different amounts of FAMEs, but also ensure that no more than the maximum amount of C required for graphitisation is used (1 mg in our case). Pseudo-processing standards and blanks can be run using these parameters for blank correction and quality control purposes.

5. e. Once isolated, the traps should be removed, wrapped in aluminium foil, and stored in the fridge until graphitization, as the FAMEs can demethylate under high temperatures.

3.4 Case Study 2: Trapping efficiency

The PGC trapping efficiencies of solventless trap design have been rigorously assessed using a standard solution of C_16:0 and C_18:0 FAMEs (Casanova et al. Reference Casanova, Knowles, Williams, Crump and Evershed2018). The study showed that using a 1 min trapping window across the two peaks resulted in ca. 1% of the FAMEs going into the waste trap, probably as a result of the tailing of the peaks. The remainder of each FAME, on average 98% of the total, was trapped onto the glass wool plug with 1% deposited on the glass wall. When applied to more complex FAME extracts of potsherds the trapping windows were reduced to about 30 s to avoid co-trapping of compounds eluting just after (<1 min) after the FAMEs.

Efficiency of FAME trapping is illustrated in Figure 3b. The extraction of 1.8 g and 2.3 g of powdered potsherd yielded total lipid concentrations of 2.1 mg.g^–1 and 5.3 mg.g^–1, respectively, of potsherds ROSC4690 and ROSC4678. The concentrations of the TLEs were adjusted to ∼5 µg.µL^–1 of individual FAMEs for their isolation in the pcGC. In order to evaluate the trapping efficiency, the contents of the waste trap were analyzed by GC as the trapped C_16:0 and C_18:0 were required for the ¹⁴C measurements. For sherd TLE ROSC4690 the amounts of C_16:0 and C_18:0 present in waste trap were 5.1 µg and 11.3 µg, respectively, corresponding to 1 and 2% of the FAME injected supporting the average 98% trapping efficiencies determined using standards. For the TLE of ROSC4678 the waste trap contained 15.2 µg and 21.9 µg, respectively, of C_16:0 and C_18:0 which corresponds to 8 and 10% of the FAME injected. In this case the peak tail was longer due to the higher amounts of FAMEs injected with the result that a lower proportion of the chromatographic peaks were captured by the narrower trapping windows.

Figure 3 a. Main steps of the pretreatment procedure: i. Cleaning of potsherd surface ii. Extraction of lipids from powdered ceramic on heating block iii. Solventless trapping system for isolation of single compounds by pcGC. b. Gas chromatograms of potsherd lipid extracts suitable for ¹⁴C dating (upper) with the dashed lines indicating the trapping windows required to isolate C_16:0 and C_18:0 fatty acids, and the contents of the waste traps after isolation by pcGC (lower).

This case study emphasises the importance of carefully considering the width of trapping windows in relation to the amounts of FAME injected, as trapping efficiencies will be reduced due to peak tailing, with the chromatographic peak tails transferred to the waste trap following switching. The critical judgement in trapping compounds from complex mixtures is balancing the need for peak purity (avoiding co-trapping) against trapping efficiency.

4.1 Graphitization and AMS measurements

Once the FAMEs are trapped, the glass wool plug containing the FAMEs is directly transferred into an Al foil capsule using a clean glass pipette, plunger or a wire. Graphitization and AMS analysis is carried out as described in Knowles et al. (Reference Knowles, Monaghan and Evershed2019). Briefly, we use an elemental analyser for the combustion coupled to an automated graphitization equipment (EA-AGE 3) (Wacker et al. Reference Wacker, Christl and Synal2010b), but this could also be performed using semi-automatic or manual lines depending on individual laboratory capabilities. For the pseudo-processing standards (cf part 3.2), the standard is weighed into the Al capsule then the glass wool from the trap is added prior to combustion. The FAME processing standards (bog butters) are treated in exactly the same way as a pot lipid extract.

The graphite targets are analyzed by AMS (MICADAS; Synal et al. Reference Synal, Stocker and Suter2007) alongside size-matched standards. It is commonly the case that the C_16:0 and C_18:0 FA of individual potsherds differ in abundance resulting in differing amounts being trapped. In such instances data reduction for the different sample sizes is performed in different calculation sets, so that appropriate corrections can be applied.

4.2 Correction for the derivatising methyl carbon

The FAs are converted to FAMEs during their extraction, making them amenable for GC isolation using a non-polar GC column. The methylation adds a single C atom (of fossil origin, from the methanol) to the FA that affects the measured radiocarbon date and thus requires correction. Two types of correction can be applied (Stott et al. Reference Stott, Berstan, Evershed, Bronk-Ramsey, Hedges and Humm2003): (i) a simple mass balance correction (Equation 1, referred as F¹⁴C_FA.1), or (ii) a more refined correction, which considers the fractionation occurring during the methylation reaction (Equation 2, referred as F¹⁴C_FA.2).

(1) $${F^{14}}{C_{FA.1}} = {{No.{C_{FAME}}{\rm{*}}\;{F^{14}}{C_{measured}}} \over {No.{C_{FA}}}}$$

(2) $${F^{14}}{C_{FA.2}} = {F^{14}}{C_{FA.1}}*\;\left( {{{1 + \left[ {{{ - 25 + \;{\delta ^{13}}{C_{FAME}}} \over {1000}}} \right]} \over {1 + \left[ {{{ - 25 + \;{\delta ^{13}}{C_{FA}}} \over {1000}}} \right]}}} \right)$$

Where F¹⁴C_FA.x is the fraction modern of the FA corrected for the derivative C, F¹⁴C_measured the fraction modern of the measured FAME, No.C_{FA or FAME} is the total number of C atoms in the FA or FAME and δ¹³C_{FA or FAME} the δ¹³C value of the FA or FAME (‰) recorded by GC-C-IRMS.

The efficiency of such corrections was verified by ¹⁴C dating two modern FA standards before and after methylation (no PCGC isolation). The direct measurements on the FA (Table 2) passed the χ² test at the 5% level and the weighted average is F¹⁴C_FA = 1.0430 ± 0.0015 (T’ = 1.5, T’(5%) = 9.5, ν = 4) for the C_16:0 FA and F¹⁴C_FA = 1.5037 ± 0.0015 (T’ = 0.3, T’(5%) = 9.5, ν= 4) for the C_18:0 FA. The measurements of the methylated FA passed the χ² test at the 5% level for the C_16:0 (T’ = 7.6, T’(5%) = 9.5, ν = 4) and the C_18:0 (T’ = 4.6, T’(5%) = 9.5, ν = 4). This demonstrates a good reproducibility of the methylation process within statistical expectations.

Table 2 F¹⁴C of C_16:0 and C_18:0 FA dated directly and after methylation and pcGC isolation. F¹⁴C_FA corresponds to the fatty acid, F¹⁴C_FAME to the fatty acid after methylation, F¹⁴C_FA.1 to the correction of additional methyl group using mass balance calculation, and F¹⁴C_FA.2 to the correction of the methyl group using the refined correction to account for fractionation

When applying the mass balance correction (Equation 1) then F¹⁴C_FA.1 = 1.0434 ± 0.0020 for the C_16:0 and F¹⁴C_FA.1 = 1.0528 ± 0.002 for the C_18:0 FA. The values were all identical within error to the weighted mean of direct measurements (with the exception of BRAMS-1086.2.1 which is just outside the 2-σ range) demonstrating the accuracy of the radiocarbon determinations after correction. When applying the correction including fractionation (Equation 2) then F¹⁴C_FA.2 = 1.0428 ± 000.20 for the C_16:0 and F¹⁴C_FA.2 = 1.0521 ± 0.0020 for the C_18:0 FA. These values are identical within error to the weighted average of the direct measurements, demonstrating the accuracy of the radiocarbon determinations after correction.

A difference was observed of 0.5‰ from the weighted average value of F¹⁴C_FA and F¹⁴C_FA.1, and of 0.2‰ from the average value of F¹⁴C_FA and F¹⁴C_FA.2 for the C_16:0 FA. The difference between the two corrections is 0.7‰ (i.e. 5-6 y with fossil C). For the C_18:0 FA the difference between the average values of F¹⁴C_FA and F¹⁴C_FA.1 is 0.9‰ and that between F¹⁴C_FA and F¹⁴C_FA.2 is 1.6‰. The difference between the two corrections is also 0.7‰.

Both corrections met the accuracy expected after correction as the results are statistically indistinguishable from the direct measurements. The F¹⁴C_FA.2 measure for the C_18:0 FA being above 1‰ difference from the bulk date, we suggest the simple mass balance approach (Equation 1, F¹⁴C_FA.1) introduces less variability and is sufficient in obtaining an accurate correction for the derivatising methyl group added during the extraction of lipids and we therefore adopt this one routinely.

4.3. Internal quality control and combination

Each pottery vessel produces two ¹⁴C dates: one per FA. There is therefore, an internal quality control criterion based on the identicality of the C_16:0 and C_{18 :0} FA radiocarbon ages after correction for the methanol (Casanova et al. Reference Casanova, Knowles, Bayliss, Dunne, Barański, Denaire, Lefranc, di Lernia, Roffet-Salque, Smyth, Barclay, Gillard, Claßen, Coles, Ilett, Jeunesse, Krueger, Marciniak, Minnitt, Rotunno, van de Velde, van Wijk, Cotton, Daykin and Evershed2020c). If the measurements are statistically indistinguishable at the 5% level, the two results should be combined before any calibration.

The measurements on the C_16:0 and C_18:0 FAs are not fully independent as they are extracted and methylated from the same vessel and trapped by GC at the same time, so the combination of their dates should not be calculated as a simple weighted average using their quoted uncertainties, as would be done for two independent replicates. Given the uncertainties introduced during the FA preparation are not statistically independent we calculate the uncertainty of the combined date as follows (Casanova et al. Reference Casanova, Knowles, Ford, Cramp, Sharples and Evershed2020b):

(3) $${\sigma _f} = \;\sqrt {{\sigma _{wm}}^2 + {\sigma _{ss}}^2} $$

Where σ_f is the final overall uncertainty associated with the combined measurements of the FAs, σ_wm is the combined (reduced) uncertainty from the weighted mean of measurements using only the AMS uncertainty (equivalent to σ_<Rmol,bl,f> in Wacker et al. (Reference Wacker, Christl and Synal2010a) and σ_ss is the sample scatter to account for additional uncertainties associated with sample preparation (equivalent to σ_ex). The value for σ_wm is calculated by combining the two dates after removing the sample scatter factor from their respective uncertainties.

Any two measurements that are not statistically indistinguishable should be treated with caution as this could denote contamination occurred during pretreatment or isolation. Possible causes would be deterioration of graphite ferrules in the preparative unit or inadvertent deposition of dust in the traps during the fitting/release of the traps. If a significant difference is still observed between the two FA ages in a second analysis of lipids from the same pot, this would more likely be a result of different sources of C (with different relative abundances and radiocarbon ages) contributing to the two FAs, such as the mixing of aquatic and terrestrial fats in the same vessel (see section 5.2. below for further discussion of this). If remeasurement is not possible then these values should be treated with caution.

5.1 Calibration of terrestrial animal lipid dates

For the calibration of terrestrial fats, we use the combined C_16:0 and C_18:0 measurements in calibration software such as OxCal (Bronk Ramsey Reference Bronk Ramsey2009). The potsherd dates are calibrated against the latest calibration curve available for the Northern or Southern hemisphere based on the location of the site.

If the potsherd dates are integrated into chronological models for Bayesian analyses of radiocarbon dates their position in the models is defined based on the site stratigraphy or seriation on a case-by-case basis. For instance, the CSRA of FAs from potsherds from Çatalhöyük were integrated in the model in a position defined by the stratigraphy, while the potsherds from the Grossgartach were integrated into a model based on seriation (Casanova et al. Reference Casanova, Knowles, Bayliss, Dunne, Barański, Denaire, Lefranc, di Lernia, Roffet-Salque, Smyth, Barclay, Gillard, Claßen, Coles, Ilett, Jeunesse, Krueger, Marciniak, Minnitt, Rotunno, van de Velde, van Wijk, Cotton, Daykin and Evershed2020c).

5.2 Calibration of mixed marine/terrestrial lipid dates

In some cases, the ¹⁴C dated FAs are not purely of terrestrial origin but present as mixtures with fats of marine origin. In such cases corrections for marine reservoir effects (MRE) are necessary. For calibration and correction, similar considerations to those applicable to bone collagen are applied. This means using the local deviation from the global marine curve (ΔR,) and calculating the percentage of marine products in the dated fraction (Cook et al. Reference Cook, Ascough, Bonsall, Hamilton, Russell, Sayle, Scott and Bownes2015). These considerations are published in detail in Casanova et al. (Reference Casanova, Knowles, Ford, Cramp, Sharples and Evershed2020b), so we only provide a summary here. The following steps must be undertaken:

1. a. Identification of the likely presence of marine product processing in potsherds based on the presence of aquatic biomarkers in the TLEs, δ¹³C_16:0 and δ¹³C_18:0 values, and faunal assessments.

2. b. Evaluation of the local ΔR using paired marine/terrestrial specimens at the site or using the published ΔR relevant for the spatiotemporal area.

3. c. Evaluation of δ¹³C_16:0 and δ¹³C_18:0 end-member values for modern reference terrestrial and marine species relevant to the local area. There is now a large database of reference animals for the UK, north Africa and Kazakhstan e.g. (Copley et al. Reference Copley, Berstan, Dudd, Docherty, Mukherjee, Straker, Payne and Evershed2003; Cramp and Evershed Reference Cramp and Evershed2014; Dunne et al. Reference Dunne, Evershed, Salque, Cramp, Bruni, Ryan, Biagetti and di Lernia2012; Outram et al. Reference Outram, Stear, Bendrey, Olsen, Kasparov, Zaibert, Thorpe and Evershed2009) allowing selection of values appropriate to the local range and animal species present at archaeological sites as endmembers (Figure 4a). If no published reference animals are available for the area, local modern reference values should be recorded on animals with feeding practices relevant to prehistory (Roffet-Salque et al. Reference Roffet-Salque, Lee, Timpson and Evershed2017).

   

   Figure 4 a. Compilation of reference values of modern ruminant adipose, ruminant dairy, porcine adipose fats, marine and freshwater species from the UK, Libya and Kazakhstan (Copley et al. Reference Copley, Berstan, Dudd, Docherty, Mukherjee, Straker, Payne and Evershed2003; Cramp and Evershed Reference Cramp and Evershed2014; Dunne et al. Reference Dunne, Evershed, Salque, Cramp, Bruni, Ryan, Biagetti and di Lernia2012; Outram et al. Reference Outram, Stear, Bendrey, Olsen, Kasparov, Zaibert, Thorpe and Evershed2009). Ellipses represent the 68% (1σ) of the values. b,c. Percentage of marine products in the lipid extracts expressed as probability distributions (b) box and whisker plots (c) for the potsherds BN74 and BN89. d. Calibration of reference terrestrial animal bone dates and the dates on the lipids from potsherd BN74 and BN89 uncorrected and corrected for the marine reservoir effect (From Casanova et al. Reference Casanova, Knowles, Ford, Cramp, Sharples and Evershed2020b).

4. d. Calculation of the percentage of marine products (%_marine) using δ¹³C_16:0 and δ¹³C_18:0 values and those of the local and relevant endmembers. The percentage of marine products could be simply evaluated with linear mixing of the δ¹³C_16:0 and δ¹³C_18:0 values of marine and terrestrial endmembers, however, we recommend implementing the δ¹³C_16:0 and δ¹³C_18:0 values in the software FRUITS (Fernandes et al. Reference Fernandes, Millard, Brabec, Nadeau and Grootes2014) or the ReSources IsoMemo package (https://github.com/Pandora-IsoMemo/resources).

5. e. Correction for the marine reservoir effects in the software OxCal using the Marine/mixed curve tool and the ΔR and %_marine determined. We recommend implementing the full probability distribution of the %_marine calculated in FRUITS or ReSources as a Prior file rather than the mean and standard deviation as the percentage marine.

5.3 Calibration of mixed freshwater/terrestrial lipid dates

Animal fat residues in pottery can also originate from freshwater environments such as lakes or rivers. In such systems these residues will be affected by a freshwater reservoir effect (FRE). FREs generally arise due to the introduction of old C to the aquatic system, most notably as a result of the dissolution of carbonates, known as the hard water effect (Philippsen, Reference Philippsen2013) or the ebullition of CO₂ from close volcanic activity. The measurement of such reservoir effects is time, depth, and species dependent for a given site, with high variability observed (Hajdas et al. Reference Hajdas, Ascough, Garnett, Fallon and Pearson2021; Keaveney and Reimer Reference Keaveney and Reimer2012). It is therefore extremely complex, making it essential to properly estimate the FRE at sites. It is also extremely difficult to quantify the FRE of lipids preserved in potsherds if freshwater resources were mixed with terrestrial resources.

There is currently no published example of a dataset where correction of ¹⁴C dates of lipid residues affected by a FRE has been performed. However, if such study is to be contemplated, we recommend the following:

1. a. Identification of the presence of freshwater resource processing in potsherds using combination of the specific aquatic biomarkers, stable carbon isotope values and faunal evidence. This should be done for every site in a freshwater catchment using the whole ceramic assemblage studied for ORA.

2. b. Assessment of the local geology to determine whether the water bodies are closed or open systems and if possibilities exist for dissolution of “old” C from carbonates or volcanic activity. This will give preliminary indications of whether FRE are likely to be present at sites. The FRE can then be evaluated, as before, by dating paired aquatic and terrestrial archaeological samples from the same contexts.

3. c. Evaluation the percentage of freshwater products using the using δ¹³C_16:0 and δ¹³C_18:0 values of the individual fatty acids of the pots (recorded on the same TLE submitted for dating) and those of endmember values derived from modern references relevant for the site catchment.

4. d. Correction of the FA radiocarbon dates for the FRE prior to calibration using the calculated reservoir effect and the percentage of aquatic products processed in the vessels.

5.4 Case Study 3: Calibrating and modeling mixed terrestrial and aquatic lipid dates

We illustrate here the correction for marine reservoir effects affecting lipids from two potsherds for the site of Bornais in the Outer Hebrides, UK. For this site ∼170 pottery vessels were analyzed by ORA, which revealed extensive processing of ruminant carcass, ruminant dairy and marine products in the pottery vessels. Aquatic biomarkers were identified in approximatively 50% of the vessels analyzed (Casanova et al. Reference Casanova, Knowles, Bayliss, Dunne, Barański, Denaire, Lefranc, di Lernia, Roffet-Salque, Smyth, Barclay, Gillard, Claßen, Coles, Ilett, Jeunesse, Krueger, Marciniak, Minnitt, Rotunno, van de Velde, van Wijk, Cotton, Daykin and Evershed2020c; Cramp et al. Reference Cramp, Casanova, Evershed and Bornais2020). We applied the paired dating approach to terrestrial and marine products from the same contexts to calculate the local ΔR of –65 ± 46.

We calculated the %_marine using δ¹³C_16:0 and δ¹³C_18:0 values of the pottery and those of modern reference animal species from the UK land and coastal waters as endmembers (Copley et al. Reference Copley, Berstan, Dudd, Docherty, Mukherjee, Straker, Payne and Evershed2003; Cramp and Evershed, Reference Cramp and Evershed2014). We hypothesised that pigs and other non-ruminants had not contributed significantly to the fat residues in the pottery due to their relatively low representation in the faunal record compared to other species, and only considered marine species present at the site (e.g. limpets, winkles, cod, saith etc.). We therefore, used the mean values of δ¹³C_16:0 = –30.0 ± 0.6‰ and δ¹³C_18:0 = –32.2 ± 0.6‰ for ruminant adipose fats, δ¹³C_16:0 = –29.2 ± 1.0‰ and δ¹³C_18:0 = –34.0 ± 0.9‰ for dairy fats and δ¹³C_16:0 = –22.7 ± 2.2‰ and δ¹³C_18:0 = –21.7 ± 2.5‰ for marine fats as end-members. These values were input into the FRUITS model alongside the δ¹³C_16:0 and δ¹³C_18:0 values recorded for the FAs extracted from two potsherds to obtain the proportion of marine products present in pots (Figure 4b,c). This value, alongside the percentage marine (full probability distribution file extracted from FRUITS), were inputted into OxCal using the Mix/Marine function for MRE corrections. The corrected ¹⁴C measurements give probability distributions entirely compatible with the calendar ages of terrestrial organisms from the same context (Figure 4d).

In another case study of inland sites across central Europe, we found aquatic biomarkers in lipid extracts identified as ruminant adipose and ruminant dairy products based on δ¹³C_16:0 and δ¹³C_18:0 values (Casanova et al. Reference Casanova, Knowles, Bayliss, Roffet-Salque, Heyd, Pyzel, Claßen, Domboroczki, Ilett, Lefranc, Jeunesse, Marciniak, van Wijk and Evershed2022a). Because these sites are inland but rather close to freshwater streams and lakes, FREs were possible. The absence of aquatic remains in the faunal record meant it was not possible to evaluate the FRE for the sites, hence, the ¹⁴C dates were not corrected but rather modeled in OxCal as TPQ dates (Terminus Post Quem, i.e. “date after which”). This was a cautionary approach which recognised the potential for FREs affecting the CSRA measurements.